rf309_ndimplot.py

## \ingroup tutorial_roofit_main

## \notebook

## Multidimensional models: making 2/3 dimensional plots of pdfs and datasets

##

## \macro_image

## \macro_code

## \macro_output

##

## \date February 2018

## \authors Clemens Lange, Wouter Verkerke (C++ version)

import ROOT

# Create 2D model and dataset

# -----------------------------------------------------

# Create observables

x = ROOT.RooRealVar("x", "x", -5, 5)

y = ROOT.RooRealVar("y", "y", -5, 5)

# Create parameters

a0 = ROOT.RooRealVar("a0", "a0", -3.5, -5, 5)

a1 = ROOT.RooRealVar("a1", "a1", -1.5, -1, 1)

sigma = ROOT.RooRealVar("sigma", "width of gaussian", 1.5)

# Create interpreted function f(y) = a0 - a1*sqrt(10*abs(y))

fy = ROOT.RooFormulaVar("fy", "a0-a1*sqrt(10*abs(y))", [y, a0, a1])

# Create gauss(x,f(y),s)

model = ROOT.RooGaussian("model", "Gaussian with shifting mean", x, fy, sigma)

# Sample dataset from gauss(x,y)

data = model.generate({x, y}, 10000)

# Make 2D plots of data and model

# -------------------------------------------------------------

# Create and fill ROOT 2D histogram (20x20 bins) with contents of dataset

hh_data = data.createHistogram("x,y", x, Binning=20, YVar=dict(var=y, Binning=20))

# Create and fill ROOT 2D histogram (50x50 bins) with sampling of pdf

# hh_pdf = model.createHistogram("hh_model", x, Binning=50, YVar=dict(var=y, Binning=50))

hh_pdf = model.createHistogram("x,y", 50, 50)

hh_pdf.SetLineColor("kBlue")

# Create 3D model and dataset

# -----------------------------------------------------

# Create observables

z = ROOT.RooRealVar("z", "z", -5, 5)

gz = ROOT.RooGaussian("gz", "gz", z, 0.0, 2.0)

model3 = ROOT.RooProdPdf("model3", "model3", [model, gz])

data3 = model3.generate({x, y, z}, 10000)

# Make 3D plots of data and model

# -------------------------------------------------------------

# Create and fill ROOT 2D histogram (8x8x8 bins) with contents of dataset

# hh_data3 = data3.createHistogram("hh_data3", x, Binning=8, YVar=(var=y, Binning=8), ZVar=(var=z, Binning=8))

hh_data3 = data3.createHistogram(

"hh_data3",

x,

Binning=8,

YVar=dict(var=y, Binning=8),

ZVar=dict(var=z, Binning=8),

)

# Create and fill ROOT 2D histogram (20x20x20 bins) with sampling of pdf

hh_pdf3 = model3.createHistogram(

"hh_model3",

x,

Binning=20,

YVar=dict(var=y, Binning=20),

ZVar=dict(var=z, Binning=20),

)

hh_pdf3.SetFillColor("kBlue")

c1 = ROOT.TCanvas("rf309_2dimplot", "rf309_2dimplot", 800, 800)

c1.Divide(2, 2)

c1.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

hh_data.GetZaxis().SetTitleOffset(1.4)

hh_data.Draw("lego")

c1.cd(2)

ROOT.gPad.SetLeftMargin(0.20)

hh_pdf.GetZaxis().SetTitleOffset(2.5)

hh_pdf.Draw("surf")

c1.cd(3)

ROOT.gPad.SetLeftMargin(0.15)

hh_data.GetZaxis().SetTitleOffset(1.4)

hh_data.Draw("box")

c1.cd(4)

ROOT.gPad.SetLeftMargin(0.15)

hh_pdf.GetZaxis().SetTitleOffset(2.5)

hh_pdf.Draw("cont3")

c1.SaveAs("rf309_2dimplot.png")

c2 = ROOT.TCanvas("rf309_3dimplot", "rf309_3dimplot", 800, 400)

c2.Divide(2)

c2.cd(1)

ROOT.gPad.SetLeftMargin(0.15)

hh_data3.GetZaxis().SetTitleOffset(1.4)

hh_data3.Draw("lego")

c2.cd(2)

ROOT.gPad.SetLeftMargin(0.15)

hh_pdf3.GetZaxis().SetTitleOffset(1.4)

hh_pdf3.Draw("iso")

c2.SaveAs("rf309_3dimplot.png")